

A273208


Number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 609", based on the 5celled von Neumann neighborhood.


4



1, 4, 21, 29, 72, 84, 141, 168, 248, 289, 340, 377, 477, 525, 597, 629, 808, 908, 1081, 1153, 1233, 1356, 1469, 1497, 1692, 1873, 2016, 2149, 2324, 2521, 2676, 2641, 2952, 3220, 3504, 3604, 3900, 4020, 4176, 4320, 4564, 4896, 5072, 5244, 5560, 5932, 6041
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OFFSET

0,2


COMMENTS

Initialized with a single black (ON) cell at stage zero.


REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.


LINKS

Robert Price, Table of n, a(n) for n = 0..128
Robert Price, Diagrams of the first 20 stages
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index entries for sequences related to cellular automata
Index to 2D 5Neighbor Cellular Automata
Index to Elementary Cellular Automata


MATHEMATICA

CAStep[rule_, a_]:=Map[rule[[10#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=609; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1n, k1+n]], {j, k+1n, k1+n}], {n, 1, k}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)


CROSSREFS

Sequence in context: A276400 A304770 A316513 * A273270 A273246 A273299
Adjacent sequences: A273205 A273206 A273207 * A273209 A273210 A273211


KEYWORD

nonn,easy


AUTHOR

Robert Price, May 17 2016


STATUS

approved



